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We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding…

Machine Learning · Computer Science 2023-02-09 Julius Berner , Philipp Grohs , Gitta Kutyniok , Philipp Petersen

Learning the similarity between images constitutes the foundation for numerous vision tasks. The common paradigm is discriminative metric learning, which seeks an embedding that separates different training classes. However, the main…

Computer Vision and Pattern Recognition · Computer Science 2021-09-10 Timo Milbich , Karsten Roth , Biagio Brattoli , Björn Ommer

Error backpropagation is a highly effective mechanism for learning high-quality hierarchical features in deep networks. Updating the features or weights in one layer, however, requires waiting for the propagation of error signals from…

Neural and Evolutionary Computing · Computer Science 2017-11-21 Hesham Mostafa , Vishwajith Ramesh , Gert Cauwenberghs

Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We…

Machine Learning · Computer Science 2018-05-22 Karl Ridgeway , Michael C. Mozer

The original problem of supervised classification considers the task of automatically assigning objects to their respective classes on the basis of numerical measurements derived from these objects. Classifiers are the tools that implement…

Machine Learning · Computer Science 2017-10-26 Marco Loog

Continual lifelong learning is essential to many applications. In this paper, we propose a simple but effective approach to continual deep learning. Our approach leverages the principles of deep model compression, critical weights…

Machine Learning · Computer Science 2019-10-31 Steven C. Y. Hung , Cheng-Hao Tu , Cheng-En Wu , Chien-Hung Chen , Yi-Ming Chan , Chu-Song Chen

Extensive research on formal verification of machine learning systems indicates that learning from data alone often fails to capture underlying background knowledge, such as specifications implicitly available in the data. Various neural…

Logic in Computer Science · Computer Science 2025-03-17 Thomas Flinkow , Barak A. Pearlmutter , Rosemary Monahan

Visual change detection, aiming at segmentation of video frames into foreground and background regions, is one of the elementary tasks in computer vision and video analytics. The applications of change detection include anomaly detection,…

Computer Vision and Pattern Recognition · Computer Science 2021-05-05 Murari Mandal , Santosh Kumar Vipparthi

Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming…

Machine Learning · Computer Science 2025-06-25 Mathieu Blondel , Vincent Roulet

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity…

Computer Vision and Pattern Recognition · Computer Science 2021-04-19 Matthias De Lange , Rahaf Aljundi , Marc Masana , Sarah Parisot , Xu Jia , Ales Leonardis , Gregory Slabaugh , Tinne Tuytelaars

Recent advances in Deep Learning have greatly improved performance on various tasks such as object detection, image segmentation, sentiment analysis. The focus of most research directions up until very recently has been on beating…

Computer Vision and Pattern Recognition · Computer Science 2022-11-29 Cristian Simionescu

Over the past decade, deep learning models have exhibited considerable advancements, reaching or even exceeding human-level performance in a range of visual perception tasks. This remarkable progress has sparked interest in applying deep…

Computer Vision and Pattern Recognition · Computer Science 2023-08-29 Yulin Wang , Yizeng Han , Chaofei Wang , Shiji Song , Qi Tian , Gao Huang

Continual Learning (CL) is a field dedicated to devise algorithms able to achieve lifelong learning. Overcoming the knowledge disruption of previously acquired concepts, a drawback affecting deep learning models and that goes by the name of…

Computer Vision and Pattern Recognition · Computer Science 2023-01-04 Francesco Pelosin

While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…

Machine Learning · Computer Science 2019-08-27 Tomaso Poggio , Andrzej Banburski , Qianli Liao

Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…

Machine Learning · Computer Science 2025-09-23 Sri Satish Krishna Chaitanya Bulusu , Mikko Sillanpää

Arguably the key reason for the success of deep neural networks is their ability to autonomously form non-linear combinations of the input features, which can be used in subsequent layers of the network. The analogon to this capability in…

Machine Learning · Computer Science 2020-12-09 Johannes Fürnkranz , Eyke Hüllermeier , Eneldo Loza Mencía , Michael Rapp

In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores…

Machine Learning · Computer Science 2023-05-24 Francesco Marchetti , Sabrina Guastavino , Cristina Campi , Federico Benvenuto , Michele Piana

The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…

Artificial Intelligence · Computer Science 2011-05-30 D. Calvanese , M. Lenzerini , D. Nardi

Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Although important steps have been taken to realize the…

Neural and Evolutionary Computing · Computer Science 2020-12-09 François-Xavier Vialard , Roland Kwitt , Susan Wei , Marc Niethammer

Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…

Logic · Mathematics 2009-03-23 Saharon Shelah